Method and apparatus for electromagnetically containing a plasma



Sept. 16, 1969 G. L. CANN 3,467,885

METHOD AND APPARATUS FOR ELECTROMAGNETICALLY CONTAINING A PLASMA Filed May 20, 1965 2 Sheets-Sheet 1 INVENTOR, GORDON L. CANN Sept. 16, 1969 cs. CANN 3,467,835

METHOD AND APPARATUS FOR ELECTROMAGNETICALLY CONTAINING A PLASMA Filed May 20, 1965 2 Sheets-Sheet 2 FIG. 2

K INVENTOR GORDON L. CANN nite Stat METHOD AND APPARATUS FOR ELECTRO- MAGNE'HCALLY CONTAINING A PLASMA Gordon L. Cann, Laguna Beach, Calif., assignor, by

mesne assignments, to Xerox Corporation, a corporation of New York Filed May 20, 1965, Ser. No. 457,414 Int. Cl. H01j 7/24; Hb 31/26 US. Cl. 315111 2 Claims ABSTRACT OF THE DISCLOSURE A method and apparatus for plasma containment is disclosed in which a longitudinally continuous magnetic field symmetrical about an axis converges the plasma produced by a radial electric discharge at a single axial location to a remote pinch and allows it to diverge thereafter.

This application relates to methods and apparatus for plasma containment.

There are many situations where it is desirable to produce sustained high temperatures greatly in excess of the melting point of structural materials. These include the spectroscopic investigation of atomic structure, routine spectroscopic analysis, the study of chemical reactions, the generation of neutrons, and the study or utilization of thermonuclear reactions. Known or contemplated methods of producing extra high temperature involve generation of such temperatures in a body of plasma, which is a body of highly ionized electrically neutral gas having a very high electrical conductivity. The electrical properties of a plasma make it theoretically possible to effect containment by means of magnetic field rather than by physical contact with the walls of the container. The absence of such contact makes the containment possible at temperatures far above the melting points of all structural materials and without excessive heat losses to such containers. Many magnetic containment schemes have been proposed; some involve a transient or pulse type of operation while others are steady-state but require complex starting procedures. Prior methods involve the use of complex apparatus and have not been outstandingly successful in operation.

It is accordingly an object of the invention to provide a plasma containment and heating method which is simple, capable of steady-state operation, capable of small scale operation, requires no complex starting procedures, and is effective. It is a further object of the invention to provide a plasma containment and heating method which is electrostatic as well as magnetic in character and which makes use of Hall currents. It is still a further object of the invention to provide simple and effective apparatus for containing and heating the plasma. It is still a further object of the invention to provide a high temperature plasma jet. Further objectives will become apparent upon reading a description of the invention.

FIGURE 1 is a diagrammatic sectional view of apparatus according to the invention.

FIGURE 2 is a sectional view of the electrode assembly used in FIGURE 1.

Referring to FIGURE 1, there is shown an illustrative embodiment of the invention, including a chamber 10 which is evacuated by a vacuum pump 12 and which contains a set of coaxial magnet coils 14, 16, and 18. A single long solenoid with appropriately proportioned windings can be used, but it is more convenient to use a set of individual coils as shown. Each coil 14 to 18 has an associated high current power supply 22, 26 respectively. The coils are fluid cooled and each is provided with cooling tubes 30 through which water or other coolant is circulated by pump 32 which also circulates the coolant 3,467,885 Patented Sept. 16, 1969 through a heat exchanger 34 to remove heat generated in the coils and also heat carried by or generated in the plasma. A cooling baffle 20 may also be provided as shown adjacent to magnet coils 18. The resulting magnetic field is arbitrarily divided into three regions identified as (a), (b), and (c). In region (a) the magnetic field lines should be relatively parallel, but can converge or diverge slightly. In region (b), however, the field lines should converge so that the average axial magnetic field strength is a maximum at the downstream end of region (b). In region (0), the magnetic field lines should diverge. The junction of regions (b) and (0) can be referred to as magnetic pinch. The illustrated magnetic field configuration can be termed an electromagnetic nozzle, since the processes occurring in a plasma confined therein are similar to those occurring to an ordinary gas in an axi-symmetric Laval nozzle.

Chamber 10 can also be located inside the magnet coil if it is constructed of non-magnetic material in order that the external coils may provide the necessary magnetic field Within the chamber. An electrode assembly 36 is positioned axially within chamber 10 and facing to the right. Electrode assembly 36 is located within the longitudinally continuous field generated by coils 14 to 18 and more specifically is located in region (a) and illustrativcly Within coil 14. The electrode assembly includes a tapered or pointed cathode 40 surrounded by a concentric annular anode 42. A gas supply channel 44 introduces a suitable gas such as hydrogen from a source 46 into the space between the cathode and anode, and a DC power supply 48 is connected between a cathode and anode. Conventional supporting means, not shown, will be included in chamber 10 to position and support electrode assembly 36, magnet coils 14 to 18, cooling baffle 20, etc. and conventional electrical and fluid lead-throughs may be used to introduce the necessary electrical currents and gasses into an outer chamber 10 without breaking the vacuum therein.

A suitable electrode structure is shown in somewhat greater detail in FIGURE 2. Cathode 40 is constructed of tungsten, and like most structures in the figure, will normally be axially symmetric. It is mounted in a metal heat sink 50 which, in turn, is mounted at the end of a cathode support and cooling water conduit 52 which is sealed into phenolic support block 54 by sealing rings 56. A cathode cooling water inlet 58 is shown at the hack of conduit 52. A cathode cooling water outlet will communicate with a cavity 60 in support block 54 that is out of the plane of the drawing and not shown. It will be understood that various other cooling water passages will not appear in the drawing for the same reason. A boron nitride insulator 62 is mounted on cathode conduit 52 and surrounds cathode 40 while leaving the tip portion exposed. Cathode 40 is bored to receive a hollow tubular pressure tap 64 located within the cathode water conduit 52. Cathode 40 contains one or more small passages 66 which connect the pressure taps 64 to the exterior surface of the cathode 40 to the cathode insulator 62 which is itself provided with a gas passage, or preferably a plurality of circumferentially disposed passages 68 which communicate with the front face of the insulator and are connected to a feed tap 44 in support block 54. Either passages 66 or 68 may be used to introduce a fluid to the space adjacent to the cathode, but it is generally preferable to introduce the fluid through passages 68 and to use passages 66 for measuring the pressure adjacent to cathode 40.

A water cooled copper anode assembly 42 is mounted on the support block 54 and is insulated from cathode 40 by insulator 62. The anode has a concave conical outer face and a cylindrical inner surface which joins the outer face along a sharp edge. Illustratively, the diameter of the inner surface is 1.5 cm. Anode 42 is connected to an electrically conductive water inlet conduit 72 and to an outlet conduit, not shown. It is also provided with one or more passages 74 which communicate with the inner surface of the anode and are connected to an anode pressure tap 76 which permits measurements of pressures adjacent to the anode. Other types of coaxial electrode assemblies may be used and it will be understood that the particular size, configuration, and materials described in FIGURE 2 are for illustrative purposes only. It is merely necessary that the central cathode tip be associated with a surrounding ring anode located axially adjacent to the cathode tip.

In operation, chamber is evacuated, magnet coils 14 to 18 are energized, a gas is fed from source 46 through channel 44 to electrode assembly 36 and power supply 48 is energized to strike an electrical arc between cathode 40 and anode 42. A plasma, i.e., positive ions and negative electrons, is thereby generated and fills the region to the right of electrode assembly 36. Because of the magnetic field existing in the device, the plasma electrons are constrained to execute small diameter cyclotron oscillations about the magnetic lines of force. A magnetic field will be chosen in relation to the plasma pressure in 'accordance with conventional principles so that the electron orbital radius will be substantially less than the plasma column radius and so that the mean free path of the electrons will substantially exceed the electron orbital circumference, collision deflection, i.e., 21rw 7' is very large compared to unity, where w is the angular cyclotron frequency for electrons and T is the mean time between electron collisions. This condition is not difficult to achieve in a practical device because the effective collision cross section decreases at high plasma temperatures. Under this condition, as is known in the plasma art, the electric lines of force are essentially constrained to follow the magnetic lines of force. From a macroscopic point of view, a high temperature plasma in a magnetic field exhibits a high degree of electrical conductivity parallel to the magnetic lines of force, but a very low degree of conductivity perpendicular to the line of force. The reality of this effect can readily be demonstrated. In some cases, it is also preferred that w 'r for the ions be small compared to unity so that the ion collision mean free path is large compared to the plasma radius. This condition is readily obtained in a practical plasma. Also, as high a vacuum as possible should be maintained in chamber 10 to minimize heat losses from the plasma.

Under the described conditions, a confined column of plasma 80 is formed in region (b) and can be visually observed through portholes in chamber 10. The containment mechanism in region (b) can now be simply described. Electrons are confined to orbits about the magnetic lines of force and the ions and electrons are each urged outwards by the radial pressure gradient in the column. The constraining force on the ions is primarily the radial electric field rather than a force associated with the magnetic field. Considering a section taken normal to the axis of the device in region (b), it is obvious that the positive ions find themselves in an electrostatic potential well from which they are unable to escape unless they have an energy higher than the potential drop between the axis of the plasma and the outside thereof. This is in marked contrast to the prior schemes of plasma containment and has several favorable consequences. One of these is that the diameter of the containment device and the strength of the magnetic field need not be such as to provide ion orbital radii which are small in comparison to the device radius. The radial electric field exerts an outward force on the plasma electrons but they cannot move outward except by losing energy in collisions with plasma ions, neutral atoms, or other electrons. This is a useful effect since it serves to heat the plasma and particularly the ionic component. The interaction of the radial current flow with the longitudinal magnetic field also creates a rotating Hall current and a plasma rotation which tends to maintain the plasma column in rotation about its axis and to provide con- 4 fining forces for the electrons because of the interaction between the circumferential Hall current and the axial magnetic field. The Hall current also generates a magnetic field which opposes that of magnets 14 to 18.

The situation in region (a) in the vicinity of electrode assembly 36 is somewhat more complex. A diffuse arc is formed between the cathode tip and the anode ring and extends considerably downstream from the electrodes themselves. It is believed that the electrons produced at the cathode travel some distance along the axis of the device before diffusing outward as suggested in FIGURE 1. When all three spatial coordinates are considered, this picture must be substantially modified to account for the action of the magnetic field. The radial component of the current will interact with the longitudinal component of the magnetic field to produce strong confining Hall currents which circulate around the axis of the device. These currents arise in the absence of a circumferential electric field because of the J xB interaction between the radial current density J, and the longitudinal magnetic field B x representing the conventional vector cross product. These Hall currents are in the same direction as those noted previously in discussing equilibrium in region (b) of the plasma column. The circumferential Hall currents will interact in a similar manner with the radial component of the magnetic field to produce an axial acceleration. Axial Hall current plasma acceleration is not considered beneficial in this invention and, therefore, the magnetic field lines in region (a) should be reasonably parallel.

There is also an ion current formed at the anode which travels longitudinally away from the anode before diffusing towards the center of the plasma column and returning to the cathode. It is believed that near the anode the ions carry the bulk of the current in the arc discharge because the plasma is not fully ionized and the ions are much more weakly coupled to the magnetic field than the electrons. Hence, the electromagnetic confining force on the plasma is largely independent of the strength of the applied magnetic field, provided it is large enough so that w r w is much greater than 1. This effect is enhanced by the mass injection or gas fiow 84 which is supplied to the electrode assembly from gas source 46. Some of this gas is ionized by the arc discharge or by heat conduction from the plasma and contributes to the plasma. Some of the gas is not ionized and escapes from the plasma column in the manner indicated in FIGURE 1. This gas flow provides several important functions. One important function is simply that of cooling the electrodes. The gaseous atoms also collide with the plasma ions and further decouple them from the magnetic field. The gas flow also serves other closely related important functions. In the absence of the gas flow the entire plasma column would be set into very rapid rotation by the electromagnetic torque and the resulting counter EMF between cathode and anode would then limit the flow of further current or energy into the system. On the other hand, the ion rotational frequency would approach the electron rotational frequency thus reducing the net Hall currents and the resulting stabilizing and containing effect in region (b). Finally, under these conditions, much of the plasma energy would be in the form of rotational kinetic energy rather than the desired thermal energy. The above mentioned gas fiow carries off some of the angular momentum from the plasma column and this acts as a brake or counter-torque on the plasma column, particularly on the ions. This effect preserves the Hall current, thermalizes the ion kinetic energy, and permits the plasma column to absorb energy from the arc current. The torque acting on the plasma column is essentially the product of the magnetic field and the arc current. Assuming that the unionized gas reaches equilibrium with the plasma before escaping outward, the plasma angular velocity can be calculated as Bi/m where m represents the total gas freeput from the external source 46 and i is the arc current at the electrode assembly 36. Accordingly, it is generally preferred to minimize the magnetic field B so that the magnetic pressure B /2 (where n is the permeability of free space) is not excessively greater than the actual gas pressure. For small-scale experiments, as will be described hereafter, the plasma rotational velocity will be on the order of 1 million rotations a second. As noted previously, this macroscopic plasma rotation is believed to have a significant effect in stabilizing the operation of the device. Finally, the gas flow establishes a pressure gradient away from the electrode assembly which helps to reduce heat losses from the plasma to the electrodes.

A brief theoretical analysis of the invention will be given later on. The analysis is not as complete as has been made on certain other plasma containment invention, but the present invention is distinguished, among, other things, from prior are devices in that it is capable of. successful operation on a normal laboratory scale and has in fact been so operated. Of course, the analysis will show that with this invention as with others, containment efliciency and plasma temperature tends to rise if equipment is constructed on a larger scale and operated at higher power.

In an experiment corresponding to FIGURE 1, three magnet coils were employed corresponding generally to coils 14, 16, and 18. Each coil was 3% long by 3 inside diameter and wound in such a way that in coil 14 one gauss was produced in the center of an isolated coil for each ampere of exciting current and in coils 16 and 18 three gauss were produced for each ampere. The electrode assembly corresponded to that of FIGURE 2 and the internal diameter of the anode was 1.5 centimeters. Other types of coaxial electrode assemblies may be used. The face of coil 14 was spaced 3" from the adjacent face of coil 16 and the adjacent faces of coils 16 and 18 were spaced 1" apart. The face of anode 42 was recessed of an inch within coil 14. A current of 2,410 amperes was applied to coil 14 and a current of 1,700 amperes to coils 16 and 18. The are current was 810 amperes and the arc voltage 105 volts. Hydrogen gas was introduced at the rate of 0.02 gram per second and the pressure in chamber was .09 millimeter. Under these conditions a stable plasma column was obtained having a pressure of 30 millimeters as measured at cathode pressure tap 64. The plasma column was essentially colorless with a sharply defined outer surface which was surrounded by a brilliant red globe believed due to atomic or molecular hydrogen.

It might be assumed that in an open-ended device of this character the plasma losses would be prohibitably high due to the flux from region (b) to region (c). Unexpectedly, however, both experiment and theoretical analysis indicate that this is not so and that the present invention has certain advantages. In this invention, the apparatus would be proportioned so that the are current has all crossed from the anode sheet to the cathode jet entirely within regions (a) and (b). The plasma fiow will be subsonic in regions (a) and (b) and become sonic at the pinch, or transition between region (b) and (c). Accordingly, a favorable relation can be established between the plasma pressure, the plasma mass flow rate, the area of the magnetic nozzle, and the power transfer to the gas. Much of the energy of the plasma escaping into region (0) can be recovered in cooling baffle 20 or the energy can be extracted in a magnetohydrodynamic electricity genera-tor as described in connection with co-pending application entitled Controlled Fusion Devices, Ser. No. 373,220, filed June 8, 1964, or the escaping plasma can be used for propulsive purposes in space applications.

The maximum attainable plasma temperature may be calculated as (MKS units).

T mionization temp.-20,000 K.

'y=ratio of specific heats=% M =mass of ion |e|=charge of electron I=current In this equation, :1 is the percent of and is given by:

power radiated This indicates that the length is essentially proportional to the square of the total magnetic flux in the plasma column and since the plasma column follows the field line there is no stringent requirement to have a strong magnetic field at the junction of regions (b) and (c) or to attempt to pinch the plasma column down to a very small diameter.

The power absorbed in the anode 42 can be calculated where K thermal conductivity (parallel to B). Thus, in the present invention the anode power dissipation does not rise as fast with increasing plasma temperature as might be expected. It is believed that this is because in the present invention much of the plasma heat energy is carried away from the electrodes by convection rather than into the electrodes by conduction.

Any gas or gasifiable material may be used to form the plasma, depending on the intended use of the plasma. Where neutron generation or power production is intended a hydrogenic gas will be used, particularly deu terium or tritium or mixtures thereof. Although a theory of operation has been proposed, the invention is not predicated on the validity of this theory since operability is a demonstrated fact. Furthermore, it appears likely that the theoretical mechanism of operation may vary under different operating conditions. Many variations may be made to a described embodiment without departing from the novel concept of the invention. Thus, complete symmetry about a liner axis is preferred, but departures from this symmetry can be tolerated and the axis itself can be curved since the discharge will follow the magnetic field whether straight or not. The magnetic coils can be other than solenoidal or cylindrical as by being wound on conical forms, and permanent magnets may be used within the limits of their technology. It is also possible to use an alternating magnetic field provided that the frequency f is high enough so that the period 1/ f is small compared to the average residence time of an ion in the plasma column. This represents another mechanism for introducing energy into the plasma. Other variations in size, configuration, operating conditions and the like are encompassed by the invention as defined in the claims.

I claim:

1. The method of electromagnetically containing a body of high temperature plasma to which a macroscopic rotation about an axis is imparted in which the magnetic field, temperature, and plasma density are such that 21rw 1- is greater than 1 where w is the cyclotron angular velocity for electrons and 'r is a mean time between collisions for electrons comprising:

(a) producing a longitudinally continuous magnetic field substantially symmetrical about said axis such that the magnetic containment pressure is greater than but of the same order of magnitude as the plasma pressure,

(b) maintaining a radial electric discharge at a single axial location within said magnetic field substantially symmetrical about said axis and having a discharge radius less than the cyclotron radius for ions in said plasma, the outside of said discharge being positive with respect to the inside,

(c) supplying an ionizable gas to said discharge,

(d) converging the magnetic field lines of said axial magnetic field to a pinch downstream of and remote from said single axial discharge location, and

(e) diverging the magnetic field lines of said axial magnetic field downstream of said pinch.

2. A plasma containment apparatus for electromagnetically containing a body of high temperature plasma to which a macroscopic rotation about an axis is imparted in which the magnetic field, temperature, and plasma density within said apparatus is such that zn'w 'r is greater than 1 where w is the cyclotron angular velocity for electrons and F is the mean time between collisions for elecrons comprising:

(a) a chamber,

(-1)) means to evacuate said chamber,

(c) magnetic coil means to produce a longitudinally continuous magnetic field substantially symmetrical about said axis within said chamber, said magnetic field being of such magnitude that the magnetic containment pressure produced thereby is greater than but of the same order of magnitude as the plasma pressure, and said magnetic field means converging the lines of force of said magnetic field to a pinch and diverging said lines of force thereafter,

(d) a single plasma arc generator disposed within said magnetic field on said axis substantially symmetrical thereabout, upstream of and remote from said pinch, said generator comprising a central cathode electrode and an anode electrode encircling said cathode at a discharge radius less than the cyclotron radius for H ions in said plasma, said generator including at least one passage terminating between said cathode and anode, the distance from said single plasma arc generrator to said pinch being so related to the magnetic field strength that all current flowing between said cathode and said anode does so in the region between said arc generator and said pinch,

(e) gas supply means to introduce a plasma forming gas through said passage,

(f) power supply means to maintain an arc discharge between said anode and said cathode, and with said plasma arc generator constituting the sole means for maintaining an inwardly radial electric field within said plasma, and

(g) energy utilization means disposed substantially along said axis on the opposite side of said pinch from said single plasma arc generator.

References Cited UNITED STATES PATENTS 2,945,119 7/1960 Blackman 315-111 X 2,992,345 7/1961 Hansen 3l5-111 X 3,104,345 9/1963 Wilcox et al 313161 X 3,209,189 9/1965 Patrick 313231 X 3,226,592 12/1965 Gough et al. -202 X JAMES W. LAWRENCE, Primary Examiner RAYMOND F. HOSSFELD, Assistant Examiner US. (:1. X.R. 

